Gravitational waves (GWs) provide a new avenue to test Einstein’s General
Relativity (GR) using the ongoing and upcoming GW detectors by measuring the
redshift evolution of the effective Planck mass proposed by several modified
theories of gravity. We propose a model-independent, data-driven approach to
measure any deviation from GR in the GW propagation effect by combining
multi-messenger observations of GW sources accompanied by EM counterparts,
commonly known as bright sirens (Binary Neutron Star(BNS) and Neutron Star
Black Hole systems(NSBH)). We show that by combining the GW luminosity distance
measurements from bright sirens with the Baryon Acoustic Oscillation (BAO)
measurements derived from galaxy clustering, and the sound horizon measurements
from the Cosmic Microwave Background (CMB), we can make a data-driven
reconstruction of deviation of the variation of the effective Planck mass
(jointly with the Hubble constant) as a function of cosmic redshift. Using this
technique, we achieve a precise measurement of GR with redshift (z) with a
precision of approximately $7.9%$ for BNSs at redshift $z=0.075$ and $10%$
for NSBHs at redshift $z=0.225$ with 5 years of observation from LVK network of
detectors. Employing $CE&ET$ for just 1 year yields the best precision of
about $1.62%$ for BNSs and $2%$ for NSBHs at redshift $z=0.5$ on the
evolution of the frictional term, and a similar precision up to $z=1$. This
measurement can discover potential deviation from any kind of model that
impacts GW propagation with ongoing and upcoming observations.
The Future of Testing Einstein’s General Relativity Using Gravitational Waves
Gravitational waves (GWs) offer a promising avenue to test Einstein’s General Relativity (GR) through the measurement of the redshift evolution of the effective Planck mass, as proposed by modified theories of gravity. In this article, we present a model-independent, data-driven approach to detect any deviations from GR in the propagation of GWs by combining multi-messenger observations of GW sources with electromagnetic (EM) counterparts, known as bright sirens. Specifically, we focus on Binary Neutron Star (BNS) and Neutron Star Black Hole (NSBH) systems.
We demonstrate that by combining measurements of the GW luminosity distance from bright sirens with Baryon Acoustic Oscillation (BAO) measurements obtained from galaxy clustering and sound horizon measurements from the Cosmic Microwave Background (CMB), we can reconstruct the variation of the effective Planck mass (alongside the Hubble constant) as a function of cosmic redshift in a data-driven manner. This approach allows us to achieve a precise measurement of GR with redshift.
Potential Challenges and Opportunities
- Challenge: The precision of the measurement is contingent upon the duration of observation from the LVK network of detectors. Five years of observation yields a precision of approximately 7.9% for BNSs at redshift z=0.075 and 10% for NSBHs at redshift z=0.225.
- Opportunity: Increasing the observation time to just 1 year using $CE&ET$ can significantly enhance precision. In this scenario, a precision of approximately 1.62% for BNSs and 2% for NSBHs at redshift z=0.5, and a similar precision up to z=1, can be achieved.
- Potential Challenge: The measurement aims to discover potential deviations from any model that impacts GW propagation. As such, it may encounter theoretical models or phenomena that were not previously considered, potentially leading to unexpected outcomes or new areas of investigation.
- Opportunity: Ongoing and upcoming observations provide opportunities to uncover new physics and refine our understanding of gravity by detecting and characterizing any deviations from GR.
In conclusion, this data-driven approach offers a promising roadmap for testing Einstein’s General Relativity using gravitational waves. By combining multi-messenger observations, including bright sirens, with BAO and CMB measurements, we can reconstruct the variation of the effective Planck mass with redshift and achieve precise measurements of GR at different cosmic redshifts. While challenges may arise in terms of observation duration and potential theoretical deviations, the opportunities for enhancing precision, discovering new physics, and refining our understanding of gravity outweigh these challenges.